The evolution of graphics rendering technology has led to the development of procedural techniques for describing various steps in the rendering process. Procedural geometry is useful as a mechanism for producing arbitrarily complex geometry from compact descriptions. For a simple example, a cube object can be represented passively, as a polygonal representation comprising a list of eight vertexes and six sides. However, a more-compact, procedural representation can be developed where the cube becomes the result of a cube-generating procedure, which needs as input only position coordinates and a size. In another example, curves can be described according to Bézier control points, allowing a complex path to be mathematically described with only a few data points. Thus, geometric procedures often provide a useful, compact way to represent shapes, avoiding the access and transfer of many points of data. More complex procedures, such as rotations or splines, offer even greater compression of data. Other processes, such as shading and texture also take advantage of procedural techniques. Indeed, programmable procedural shaders are seen by some as a most efficient way to tackle graphical rendering problems.
However, conventional graphics display or graphics processor unit (“GPU”) architectures enforce a divide between procedural geometry and procedural appearance (such as procedural shaders and texture) by means of a processing chain that operates on fixed, passive polygonal primitives. A common approach is to relegate procedural geometry to the prerasterization stages, to expand the procedures into polygons, and to devote a large amount of bandwidth to feeding polygons to the transformation and setup stages of the graphics processor.
These limitations can lead to visible and undesirable artifacts. One situation for which an optimal solution has not yet been found involves dealing with changes in resolution when zooming in on shapes. As an example, consider rendering a triangle, whose vertices are the control points of a quadratic Bézier curve, such that the parts inside and outside the curve are shaded differently, particularly when the triangle can be embedded in a three dimensional space and viewed in perspective.
One solution might be to densely sample the curve, forming many more smaller triangles and shading the inside and outside triangles accordingly. An alternative might be to create a texture image of the untransformed triangle and mark texture pixels, or texels, as either inside or outside, and then render the triangle with this texture. While both of these approaches will work, they both introduce sampling artifacts under zoom. When zooming in on the triangle using the sampled curve, a view will see the facets of the piecewise linear approximation to the curve. If a viewer instead zooms in on the textured triangle, he or she would see the texels of the underlying texture image grow as the texture resolution fails to keep up with the perspective under zoom.